Q1: Two angles are complementary. If one angle measures 35°, what is the measure of the other angle? (a) 55° (b) 65° (c) 145° (d) 325°
Solution:
Ans: (a) Explanation:Complementary angles are two angles whose measures add up to 90°. To find the other angle, subtract 35° from 90°: \(90° - 35° = 55°\)
Q2: What is the measure of an angle that is supplementary to an angle of 128°? (a) 52° (b) 62° (c) 232° (d) 308°
Solution:
Ans: (a) Explanation:Supplementary angles are two angles whose measures add up to 180°. To find the supplementary angle: \(180° - 128° = 52°\)
Q3: In the diagram, two parallel lines are cut by a transversal. If one of the alternate interior angles measures 73°, what is the measure of the other alternate interior angle? (a) 73° (b) 107° (c) 17° (d) 90°
Solution:
Ans: (a) Explanation: When two parallel lines are cut by a transversal, alternate interior angles are congruent (equal in measure). Therefore, the other alternate interior angle also measures 73°.
Q4: Two lines intersect to form four angles. If one angle measures 42°, what is the measure of the vertically opposite angle? (a) 138° (b) 42° (c) 48° (d) 90°
Solution:
Ans: (b) Explanation:Vertically opposite angles (also called vertical angles) are equal in measure. When two lines intersect, the angles across from each other are congruent. Therefore, the vertically opposite angle is also 42°.
Q5: Two parallel lines are cut by a transversal. If a corresponding angle measures 115°, what is the measure of its corresponding angle on the other parallel line? (a) 65° (b) 115° (c) 75° (d) 25°
Solution:
Ans: (b) Explanation: When parallel lines are cut by a transversal, corresponding angles are congruent. This means they have the same measure. Therefore, the corresponding angle also measures 115°.
Q6: The sum of three angles in a triangle is always equal to: (a) 90° (b) 180° (c) 270° (d) 360°
Solution:
Ans: (b) Explanation: The angle sum property of a triangle states that the three interior angles of any triangle always add up to 180°. This is a fundamental property of all triangles.
Q7: Two parallel lines are cut by a transversal. One of the interior angles on the same side of the transversal measures 68°. What is the measure of the other interior angle on the same side? (a) 68° (b) 112° (c) 22° (d) 122°
Solution:
Ans: (b) Explanation:Co-interior angles (also called consecutive interior angles or same-side interior angles) are supplementary when formed by parallel lines and a transversal. They add up to 180°: \(180° - 68° = 112°\)
Q8: An exterior angle of a triangle measures 125°. If one of the non-adjacent interior angles is 55°, what is the measure of the other non-adjacent interior angle? (a) 70° (b) 60° (c) 80° (d) 65°
Solution:
Ans: (a) Explanation: The exterior angle theorem states that an exterior angle of a triangle equals the sum of the two non-adjacent interior angles. So: \(125° = 55° + x\) \(x = 125° - 55° = 70°\)
Section B: Fill in the Blanks
Q9: Two angles whose measures add up to 90° are called __________ angles.
Solution:
Ans: complementary Explanation:Complementary angles are defined as a pair of angles whose sum equals 90°. For example, 30° and 60° are complementary angles.
Q10: When two lines intersect, the angles that are across from each other are called __________ angles and are always equal in measure.
Solution:
Ans: vertically opposite (or vertical) Explanation:Vertically opposite angles are formed when two lines intersect. These angles are always congruent to each other.
Q11: The sum of all interior angles in any triangle is always __________ degrees.
Solution:
Ans: 180 Explanation: This is the angle sum property of triangles. No matter what type of triangle it is (acute, obtuse, or right), the three interior angles always sum to 180°.
Q12: Two angles whose measures add up to 180° are called __________ angles.
Solution:
Ans: supplementary Explanation:Supplementary angles are defined as a pair of angles whose sum equals 180°. For example, 120° and 60° are supplementary angles.
Q13: When two parallel lines are cut by a transversal, the angles on matching corners are called __________ angles.
Solution:
Ans: corresponding Explanation:Corresponding angles occupy the same relative position at each intersection where the transversal crosses the parallel lines. These angles are congruent when the lines are parallel.
Q14: An angle that measures exactly 90° is called a __________ angle.
Solution:
Ans: right Explanation: A right angle is defined as an angle that measures exactly 90°. It is often marked with a small square in geometric diagrams.
Section C: Word Problems
Q15: Sarah is measuring two angles that form a linear pair (supplementary angles on a straight line). One angle measures 72°. What is the measure of the other angle?
Solution:
Ans: A linear pair consists of two adjacent angles that form a straight line, so they are supplementary and add up to 180°.
Given: One angle = 72° Let the other angle = \(x\)
Q16: In a triangle, one angle measures 48° and another angle measures 67°. Find the measure of the third angle.
Solution:
Ans: Using the angle sum property of triangles, the sum of all three angles equals 180°.
Given: First angle = 48°, Second angle = 67° Let the third angle = \(x\)
\(48° + 67° + x = 180°\) \(115° + x = 180°\) \(x = 180° - 115°\) \(x = 65°\)
Final Answer: 65°
Q17: Two parallel streets are crossed by a third street (transversal). At the first intersection, one of the angles formed measures 132°. What is the measure of the alternate interior angle at the second intersection?
Solution:
Ans: When parallel lines are cut by a transversal, alternate interior angles are congruent.
Given: One alternate interior angle = 132°
Since alternate interior angles are equal when lines are parallel: The other alternate interior angle = 132°
Final Answer: 132°
Q18: Marcus drew two complementary angles. If one angle is 28° larger than the other, find the measure of both angles.
Solution:
Ans: Complementary angles add up to 90°.
Let the smaller angle = \(x\) Then the larger angle = \(x + 28°\)
Q19: Two railway tracks run parallel to each other. A third track crosses both at an angle. If one of the co-interior angles measures 73°, what is the measure of the other co-interior angle on the same side of the transversal?
Solution:
Ans: When parallel lines are cut by a transversal, co-interior angles (same-side interior angles) are supplementary and add up to 180°.
Given: One co-interior angle = 73° Let the other co-interior angle = \(x\)
Q20: An exterior angle of a triangle measures 143°. If the two non-adjacent interior angles are in the ratio 5:6, find the measure of each of these interior angles.
Solution:
Ans: By the exterior angle theorem, an exterior angle equals the sum of the two non-adjacent interior angles.
Given: Exterior angle = 143° Ratio of non-adjacent interior angles = 5:6
Let the angles be \(5x\) and \(6x\)
\(5x + 6x = 143°\) \(11x = 143°\) \(x = 13°\)
First angle = \(5 × 13° = 65°\) Second angle = \(6 × 13° = 78°\)
Verification: \(65° + 78° = 143°\) ✓
Final Answer: The two non-adjacent interior angles measure 65° and 78°
The document Worksheet (with Solutions): Angles is a part of the Grade 7 Course Math Grade 7.
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